matlab_相控阵雷达数字去斜仿真，发射信号和回波信号，混频滤波信号，正交解调，滤波器设计 使用带通滤波器，二次时延

clc;clear all;close all; %% N=100000; %子天线个数 c=3e8; f0=10e9; lum=c/f0; d=lum/2; thetaB=pi/3; Ta0=(N-1)*d*sin(thetaB)/c; %孔径渡越时间 %% B=1e8; Tp=10e-6; fs=1e8; k=B/Tp; R0=3000; R1=3500; R2=3550; t=[0:1:4000]./fs; % t=0:1/fs:4e-5; %% 发射信号和回波信号 st=cos(2*pi*(f0*t+k*t.*t/2)).*rectpuls(t/Tp); t1=2*R1/c+Ta0; sta=cos(2*pi*(f0*(t-t1)+k*(t-t1).*(t-t1)/2)).*rectpuls((t-t1)/Tp); figure; plot(t*c/2,st,'-r'); hold on; plot(t*c/2,sta,'-b'); hold on; legend('发射信号','接收信号'); %% 接收信号和参考信号 t0=2*R0/c+Ta0; sta0=cos(2*pi*(f0*(t-t0)+k*(t-t0).*(t-t0)/2)).*rectpuls((t-t0)/Tp); figure; plot(t*c/2,sta,'-b'); hold on; plot(t*c/2,sta0,'-r'); hold on; legend('接收信号','参考信号'); %% 混频信号 %sth=cos(2*pi*(f0*(t-t1)+k*(t-t1).*(t-t1)/2)).*cos(2*pi*(f0*(t-t0)+k*(t-t0).*(t-t0)/2)).*rectpuls((t-t0)/(Tp*2)); sth=sta.*sta0; figure; plot(t*c/2,sta,'-b'); hold on; plot(t*c/2,sth,'-r'); hold on; legend('接收信号','混频信号'); %% 混频滤波信号 x1=1/2*cos(2*pi*(2*f0*t-f0*(t0+t1)+k/2*((t-t1).^2+(t-t0).^2)));%.*rectpuls((t-t1)/Tp).*rectpuls((t-t0)/Tp); %混频相加部分分析 figure; plot(t*c/2,x1,'-b'); hold on; x2=1/2*cos(2*pi*(f0*(t0-t1)+k/2*(t1.*t1-t0.*t0)+k*(t0-t1)*t));%.*rectpuls((t-t1)/Tp).*rectpuls((t-t0)/Tp); %混频相减部分分析 x3=1/2*exp(1j*2*pi*(f0*(t0-t1)+k/2*(t1.*t1-t0.*t0)+k*(t0-t1)*t)); xf1=2*pi*k*(t0-t1); xf2=2*pi*(f0*(t0-t1)+k/2*(t1.*t1-t0.*t0)); xf=-xf1/2/pi; %xf为-k*(t0-t1) plot(t*c/2,x2,'-r'); hold on; legend('混频信号相加部分','混频信号相减部分'); fft_Num=200000; %傅里叶变换分析 f=fs*(0:fft_Num-1)/fft_Num; spetrumx1=fft(x1,fft_Num); spetrumx2=fft(x2,fft_Num); figure plot(f,abs(spetrumx1),'r'); hold on; plot(f,abs(spetrumx2),'b'); hold on; Rchazhi=xf*c/2/k %目标和参考距离的差值 if Rchazhi>0 figure plot(R0+f*c/2/k,abs(spetrumx1),'r'); %转换成距离 hold on; plot(R0+f*c/2/k,abs(spetrumx2),'b'); hold on; elseif Rchazhi<=0 figure plot(R0-f*c/2/k,abs(spetrumx1),'r'); %转换成距离 hold on; plot(R0-f*c/2/k,abs(spetrumx2),'b'); hold on; end %% 经过正交解调 % xIQ=x2.*cos(2*pi*f0*t)-1j*x2.*sin(2*pi*f0*t); % spetrumxIQ=fft(xIQ,fft_Num); % spetrumx3=fft(x3,fft_Num); % % % % figure % % % plot(f,abs(spetrumxIQ),'r'); % % % hold on; % % % plot(f,abs(spetrumx2),'b'); % % % hold on; % % % plot(f,abs(spetrumx3),'y'); % % % hold on; % %%正交解调滤波 % wp=1e4*2/fs; % ws=2e4*2/fs; % rp=3; % rs=60; % [n,Wc]=buttord(wp,ws,rp,rs); % [FIL_b,FIL_a]=butter(n,Wc,'low'); % [h,w]=freqz(FIL_b,FIL_a); % H=20*log10(abs(h)); % figure % plot(w/pi*fs/2,H,'g'); % xlabel('频率/Hz');ylabel('幅度/dB');title('IIR巴特沃斯低通滤波器'); % hold on; % xIQl=filter(FIL_b,FIL_a,xIQ); % % % spetrumxIQl=fft(xIQl,fft_Num); % figure % plot(f,abs(spetrumxIQl),'b'); % hold on; % figure % plot(R0-f*c/2/k,abs(spetrumxIQl),'r'); %转换成距离 % hold on; %% 滤波器设计 使用带通滤波器 % %%带通 % wp1=(xf-4*pi/Tp)*2/fs; %带通滤波器设计失败，参数要求太严格 % wp2=(xf+4*pi/Tp)*2/fs; % ws1=(xf-8*pi/Tp)*2/fs; % ws2=(xf+8*pi/Tp)*2/fs; % wp=[wp1 wp2];ws=[ws1 ws2]; % rp=3; % rs=60; % [n,Wc]=buttord(wp,ws,rp,rs); % [FIL_b,FIL_a]=butter(n,Wc); % [h,w]=freqz(FIL_b,FIL_a); % H=20*log10(abs(h)); % figure % plot(w/pi*fs/2,abs(h),'g'); % xlabel('频率/Hz');ylabel('幅度/dB');title('IIR巴特沃斯带通滤波器'); % hold on; %低通 xfgujizhi=2*k/c*500; wp=(xfgujizhi+pi/Tp)*2/fs; ws=(xfgujizhi+10*pi/Tp)*2/fs; % wp=(xf+pi/Tp)*2/fs; % ws=(xf+10*pi/Tp)*2/fs; rp=3; rs=60; [n,Wc]=buttord(wp,ws,rp,rs); [FIL_b,FIL_a]=butter(n,Wc,'low'); [h,w]=freqz(FIL_b,FIL_a); H=20*log10(abs(h)); figure % plot(w/pi*fs/2,abs(h),'g'); plot(w/pi*fs/2,H,'g'); xlabel('频率/Hz');ylabel('幅度/dB');title('IIR巴特沃斯低通滤波器'); hold on; %% 混频信号使用滤波器滤波 sthl=filter(FIL_b,FIL_a,sth); figure; plot(t*c/2,sthl,'-b'); hold on; plot(t*c/2,sth,'-r'); hold on; legend('滤波后混频信号','混频信号'); %傅里叶变换分析 spetrumsthl=fft(sthl,fft_Num); figure plot(R0+f*c/2/k,abs(spetrumsthl),'r'); hold on; xlabel('距离/m');ylabel('频谱幅度');title('滤波后信号频谱'); figure plot(R0+f*c/2/k,20*log10(abs(spetrumsthl)),'r'); hold on; xlabel('距离/m');ylabel('频谱幅度/dB');title('滤波后信号频谱'); %% 加上二次时延 sthlTa0=sthl.*(1/2*exp(1j*2*pi*k*(t0-t1)*Ta0)); ceshi=2*pi*k*(t0-t1)*Ta0 ceshi1=1/2*exp(1j*ceshi) spetrumsthlTa0=fft(sthlTa0,fft_Num); figure plot(R0+f*c/2/k,abs(spetrumsthlTa0),'r'); hold on; plot(R0+f*c/2/k,abs(spetrumsthl),'b'); hold on; xlabel('距离/m');ylabel('频谱幅度');title('滤波后加二次时延信号频谱'); %% %% 分析两个目标 t2=2*R2/c+Ta0; sta2=cos(2*pi*(f0*(t-t2)+k*(t-t2).*(t-t2)/2)).*rectpuls((t-t2)/Tp)+sta; sth2=sta0.*sta2; sthl2=filter(FIL_b,FIL_a,sth2); spetrumsthl2=fft(sthl2,fft_Num); figure plot(R0+f*c/2/k,20*log10(abs(spetrumsthl2)),'r'); hold on; xlabel('距离/m');ylabel('频谱幅度/dB');title('滤波后信号频谱');